Replicating Edwards & Lambert (2007)'s Total Effect Model

[tom...@rhsmith.umd.edu]

Dear All,

I'm trying to replicate Edwards & Lambert (2007)'s empirical example analysis which they did in SPSS and Excel (for God knows what reason). Model goes like this: X is feedback, M is satisfaction, Z is centrality and Y is commitment. Z moderates the a path (from X to M), the b path (from M to Y) and the cprime direct path (from X to Y). Essentially Z (centrality) moderates every possible link in the model, therefore the name total effect model. 

I've been trying to write code using lavaan to fit this model. But I keep getting errors. I really appreciate someone helping me out. Thanks guys! The mean centered data looks like this. Ignore gender for now. 

Here's my code:

model=

'##path from X (Feedback) to M (Satisfaction)

Satisfaction~b1*Feedback+b2*Centrality+b3*Feedback*Centrality

##path from X (Feedback)to Y(Committment) (b4-b6 represents the direct effect moderation and b7-b8 represent the path from Sat to Commitment )

Commitment~b4*Feedback+b5*Centrality+b6*Feedback*Centrality+b7*Satisfaction+ b8*Satisfaction*Centrality

##indirect effect, first define a and b and then define product term

a:= b1+b3*Centrality

b:= b7+b8*Centrality 

ab:= a*b

##direct effect

cprime:= b4+b7*Centrality

##total effect

total:=cprime+ab

'

And the error message is "Error in lav_partable_constraints_def(partable, con = LIST, debug = debug) : 

  lavaan ERROR: unknown label(s) in variable definition(s): b3 Centrality b8"

[Edward Rigdon]

I don't believe lavaan's new parameter command works this way. A new parameter must be a function of other parameters (which are not themselves new parameters). The program is assuming that your variable label "Centrality" is part of a label identifying another parameter.  They are not, hence the error message.

--Ed Rigdon

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[Terrence Jorgensen]

A new parameter must be a function of other parameters (which are not themselves new parameters). 

User-defined parameters can be functions of other user-defined parameters, such as calculating a total effect from indirect and direct effects:

set.seed(1234)

X <- rnorm(100)

M <- 0.5*X + rnorm(100)

Y <- 0.7*M + rnorm(100)

Data <- data.frame(X = X, Y = Y, M = M)

model <- ' # direct effect

Y ~ c*X

# mediator

M ~ a*X

Y ~ b*M

# indirect effect (a*b)

ab := a*b

# total effect

total := c + ab

'

fit <- sem(model, data = Data)

summary(fit)

But Ed is right that you can't create a user-defined parameter as a function of a variable.  Modeling an interaction requires you to create product terms in your data set and include those as separate variables.  To probe the interaction (i.e., test the indirect effect at different levels of the moderator), you will have to create user-defined parameters for different levels of the moderator.  Hopefully you have specific levels of substantive interest, but if not, you could use the mean and/or 1 SD below and above the mean.  I provided a similar example in an earlier post, in which the moderator was labeled W instead of Z:

https://groups.google.com/d/msg/lavaan/RW_3TMARGhY/UF9-MBk-GKIJ

You can find it by searching "Moderated mediation" in the search bar.  To test whether the indirect effect is moderated by Z, you can either 

1. run a more-constrained model in which the indirect effects at each level of Z are constrained to be equal (e.g., ' ab0 == ab1 ') and use anova() to compare them, or 
2. create user-defined parameter(s) that are differences between the indirect effects at different levels of Z (e.g., ' ab01 := ab0 - ab1 ') 
   

Terry